How can you change the curve resolution of hair particles?
There are three different settings which control this:




3D view > Particle edit mode > Tool shelf > Options > Draw. This setting affects the curve resolution in the 3D view only while in particle edit mode.
Properties > Particle settings > Render > Steps This setting controls the number of steps in the final render.
Properties > Particle settings > Display > Color This setting controls the number of steps in the viewport, outside of particle edit mode.


The Segments setting at the top of the particle settings controls the number of control vertices there are, however doesn't affect the number of interpolation steps. Think of this like scaling and image up with Nearest interpolation; you end up with more pixels, but the result is not smoothed.